V. Choose only two (2) from the following word problems. Solve and show your
complete solution on another sheet of paper.
1. A ladder leaning against a house makes an angle of 30° with the
ground. The foot of the ladder is 7 feet from the foot of the house.
How long is the ladder?
2. If a 30 ft ramp forms an angle of 32° with the ground, how high
above the ground is the top of the ramp?
3. From the top of a tower, the angle of depression to a stake on the
ground is 60°. The top of the tower is 80 feet above ground. How far
is the stake from the foot of the tower?
4. You are in a hot air balloon that is 600 feet above the ground where
you can see your friend. If the angle from your line of sight to your
friend is 20°, how far is he from the point on the ground below the
hot air balloon?
5. A man flies a kite and lets out 100 feet of string. The angle of
elevation of the string is 500
. How high off the ground is the kite?
Answers & Comments
Answer:
1. 8.08
feet
Explanation:
The ladder, the ground and the house form a right-angled triangle, with the ladder as the hypotenuse. The trigonometric ratios can therefore be used to find its length.
Sketch
Sketch
cos
(
30
o
)
=
7
L
where L is the length of the ladder.
L
=
7
cos
(
30
o
)
≈
7
0.866=8.08